She brought me a cup of tea.

Literal

She [topic-は] me [to-に] tea [object-を] one-cup brought.

持って来る ('bring,' literally 'carry-and-come') is the deictic counterpart of 持って行く ('take,' carry-and-go). The choice of 来る vs 行く encodes the direction relative to the speaker — bringing toward, taking away from. The polite past 持って来ました fits a respectful or polite-narrative register. 一杯 (いっぱい) here is the counter for cups; it doubles as a colloquial expression for 'a drink' (一杯どう 'how about a drink?').