Verse 6 of Psalm 115 reads:
O Dómine, quia ego servus tuus: * ego servus tuus, et fílius ancíllæ tuæ.
O Lord, for I am your servant: I am your servant, and the son of your handmaid.
O Dómine (O Lord), quia (for/because) ego (I) [am] servus (servant/slave) tuus (yours) ego (I) servus (servant) tuus (yours), et (and) fílius (the son) ancíllæ (of the handmaid) tuæ (your) – I (am) your servant and the son of your handmaid
quia, conj. for, because, that. truly, surely, indeedancilla, ae, f, a handmaid, maidservant.
This verse can, like many others, be interpreted literally, in its historical context, spiritually, as it applies to us, and Christologically.
First, what does it mean to be God's slave or servant in this context? The expression 'son of your handmaid' literally indicates one who has been born in the master's own household. But in the Old Testament context, it means a Jew born of Jews, and is accordingly a mark of honour. Indeed, Chrysostom says:
He is referring not to ordinary slavery but to that in keeping with a warm disposition and affection, aflame with desire, which is the highest crown, and more illustrious than any diadem. Hence God also cites it as equivalent to the highest honor in the words, "Moses my servant has died."
The Fathers of course interpreted this as meaning within the Church, as does Cassiodorus:
Son of thy handmaid seems to have been appended to denote the Catholic Church in all its forms, for she is a handmaid in her service and a bride in her marriage. So we fittingly observe that there is no martyrdom except that gained by a servant of the Lord and a son of the Catholic Church.
We can though also apply it to Christ, for Mary is indeed the handmaid of the Lord, and Christ came to serve, taking on a lowly human nature to do so: though equal to God in his divine nature, for a time he was 'a little lower than the angels' in his human nature. This verse and the next then, provide a link back to the psalms of the morning which focus on the mystery Incarnation, reminding us of what it is we are responding to with our vows, promises and sacrifices.
St Augustine instructs us on how we should respond to this verse:
Let therefore the slave purchased at so great a price confess his condition, and say, Behold, O Lord, how that I am Your servant: I am Your servant, and the son of Your handmaid ....This, therefore, is the son of the heavenly Jerusalem, which is above, the free mother of us all (Galatians 4:26) And free indeed from sin she is, but the handmaid of righteousness; to whose sons still pilgrims it is said, You have been called unto liberty (Galatians 5:13) and again he makes them servants, when he says, but by love serve one another....
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 verse of this psalm here.