Grammar JLPT Level N3 - Lesson 1

When うち, (sometimes seen using the kanji 内(うち), or 裡(うち)) is paired with the case marking particle に, it expresses a period/space 'within' which something else will/should happen/exist. It quite often (but not always) carries the nuance of (A) being the 'best', or the 'optimal' time/space within which (B) could occur/exist. In English, うちに can simply be translated as 'while', or 'during'.
うちに may be paired with the ている form of verbs, the plain form of い-Adjectives, nouns followed by の, or な-Adjectives that are followed by な.

• 彼(かれ)と毎日(まいにち)会(あ)っているうちに、だんだんと彼(かれ)の事(こと)が好(す)きになってきた。
  As I've been meeting with him everyday, I have gradually come to like him. (As I spend more time with him every day, I have grown to like him)
• 熱(あつ)いうちに食(た)べて！
  Eat it while it's hot!
• お爺(じい)ちゃんがまだ元気(げんき)なうちに家族(かぞく)皆(みんな)で旅行(りょこう)に行(い)こう！
  Let's all go on a family trip while grandpa is still healthy!
• 今(いま)のうちに明日(あした)の準備(じゅんび)をしておこう。
  Let's get ready for tomorrow while we have time. (Before it is too late)

Unlike 間(あいだ)に, うちに expresses something that can happen/exist anywhere 'within' the span of (A), and is therefore non-specific as to where (B) is located.

• 運転(うんてん)している間(あいだ)に眠(ねむ)くなったので、コンビニで休憩(きゅうけい)をした。
  I got sleepy while driving, so I took a break at a convenience store. (While in the process of driving)
• 運転(うんてん)しているうちに眠(ねむ)くなったので、コンビニで休憩(きゅうけい)をした。
  I got sleepy while driving, so I took a break at a convenience store. (At one point while driving)