Translation:Come on, let's swim.
じゃあ is actually a contraction of (それ)では. Hence the meaning of so or then. The contraction is also used in other cases: そうじゃない = そうではない (that's not the case / that's not true).
Similarly in terms of coloquial Japanese pronunciation, the unvoiced version, -ては can contact to -ちゃ(あ). Thus, このレッスンをもういちど 復習[ふくしゅう]しなくちゃ(なりません). I've gotta review this lesson one more time.