As noted in the context of the previous verse, Verse 4 of Psalm 115 is said by the priest at Mass before he receives the Precious Blood:
Cálicem salutáris accípiam: * et nomen Dómini invocábo.
I will take the chalice of salvation; and I will call upon the name of the Lord.
Cálicem (the chalice/cup) salutáris (of salvation) accípiam (I will take/receive/accept)
calix, icis, m. cup, goblet, drinking-vessel. Pars calicis, share, portion.
salutaris, e a Savior, Helper, used of God; help, saving help, rescue, salvation,
accipio, cepi, ceptum, ere 3 to take; seize, grasp; take away; receive or grasp mentally; receive
et nomen Dómini invocábo =and I will invoke the name of the Lord
nomen, mis, n. name; God himself; the perfections of God, His glory, majesty, wisdom, power, goodness,invoco, avi, atum, are, to invoke, call upon (God); to put trust in
This is one of those verses that has multiple levels of meaning.
In the Christological sense, in the context of Monday Vespers, we can perhaps read it as Christ's acceptance, as he is about to commence his three year public mission, of all that is to come, including his suffering and death. St Robert Bellarmine, for example, tells us that:
"This is universally understood of the sufferings and passion of Christ, concerning which our Savior himself said, "Can you drink of the chalice that I shall drink?" and again, "Let this chalice pass from me;" and again, John 18, "The chalice which my Father hath given me shall I not drink it?" And it is not only in the New Testament that the word chalice is used for a bitter draught of tribulation, but it also occurs in the same sense in many passages in the Old. Thus, in Psalm 74, "For in the hand of the Lord there is a cup of strong wine, full of mixture;" and in Isaias 51, "Stand up, O Jerusalem, which has drunk at the hand of the Lord the cup of his wrath." In Jer. 25, "Take the cup of wine of this fury at my hand." In Ezech. 23, "Thus saith the Lord God: Thou shalt drink thy sister's cup deep and wide: thou shalt be had in derision and scorn, and thou shalt drink it, and drink it up, even to the dregs." In Hab. 2, "Thou art filled with shame instead of glory, drink thou also and fall fast asleep; the cup of the right hand of the Lord shall compass thee, and shameful vomiting shall be on thy glory." The just man, who loves God, then says, "When I have nothing better to offer my Lord in return for all he has conferred on one, 'I will take the chalice of salvation.' I will cheerfully drink the chalice of the Lord, however bitter it may be, whether it consists in tribulations, dangers; or even death itself. For his own honor's sake he will support me; for I know that this chalice, however bitter, will be wholesome. And, as I do not rely on my own strength, but, with God's help, can do everything, 'I will, therefore, call upon the name of the Lord' to give me the grace to drink this cup courageously."
But, following 1 Cor 10:16 (which reads, "The cup of blessing which we bless, is it not a participation in the blood of Christ?') it can also be read more generally and positively as our participation in the sacraments, as St John Chrysostom points out:
Those, then, who take the expression in a spiritual sense say it is the participation in the sacraments, whereas we for the moment keep to the literal sense and say he is referring here to libations, sacrifices and thanksgiving hymns. In olden times, you see, there were different kinds of sacrifices: there was a sacrifice of praise, for sins, and burnt offerings, for personal welfare, and peace offerings and many others. So what he means is this: While I have nothing worthy to pay, I make a payment of what I have: I shall offer to God a thanksgiving sacrifice, and make mention of him for the sake of my salvation.
This psalm is used in the Common of Martyrs, and that context, it is worth emphasizing that our offering here is dependent on God's power and the graces he gives us, as Cassiodorus points out:
This is indeed a worthy promise, but it would be hazardous presumption if it rested on human powers. Who can endow confessors with endurance of tortures except Him who deigned to accept the chalice of suffering on our behalf? To show with certainty that this is impossible for human powers, they next said: And I will call upon the name of the Lord. By relying on His help they believed that they were achieving what they thought their bodily frailty inadequate to perform. The death of martyrs is defined most beautifully and briefly as: The chalice of salvation. Chalice, because it is drunk in due measure; of salvation, because through the Lord's generosity it is served for eternal salvation. Of this chalice the Lord also said in the gospel: Can you drink the chalice that I shall drink?
O Lord through your goodness you strengthen us in grace, pouring out life through the sacraments. Strengthen us indeed so we may be worthy to drink the cup of salvation, calling on your name. Save us from our enemies O Lord, that we may render a worthy sacrifice to you.
The prayer at Mass is completed by a verse from Psalm 17:
Quid retribuam Domino pro omnibus quae retribuit mihi? Calicem salutaris accipiam, et nomen Domini invocabo. Laudans invocabo Dominum, et ab inimicis meis salvus ero.
1 Crédidi, propter quod locútus sum: * ego autem humiliátus sum nimis.
2 Ego dixi in excéssu meo: * Omnis homo mendax.
3 Quid retríbuam Dómino, * pro ómnibus, quæ retríbuit mihi?
4 Cálicem salutáris accípiam: * et nomen Dómini invocábo.
5 Vota mea Dómino reddam coram omni pópulo ejus: * pretiósa in conspéctu Dómini mors sanctórum ejus:
6 O Dómine, quia ego servus tuus: * ego servus tuus, et fílius ancíllæ tuæ.
7 Dirupísti víncula mea: * tibi sacrificábo hóstiam laudis, et nomen Dómini invocábo.
8 Vota mea Dómino reddam in conspéctu omnis pópuli ejus: * in átriis domus Dómini, in médio tui, Jerúsalem.
You can find notes on the next verses of the psalm here.