字 = 宀 (roof) over 子 (child). It first meant 'to bear/raise a child under one's roof', then extended to written characters — because compound characters are 'born' from joining simpler ones, like children born within a family.
字 is the word for a Chinese character itself — the very thing this app teaches. 汉字 (Hànzì) = 'Han characters', the Chinese writing system. 名字 (with 名, which you know) = 'name'. 写字 = 'to write characters'. There are tens of thousands of 字, but ~3,000 cover almost everything you'll read — and you're collecting them one a day.
A child (子) under a roof (宀) — characters are 'born' from smaller parts. A written CHARACTER.
汉字 (Chinese characters) number in the tens of thousands, but knowing ~3,000 lets you read a newspaper. One a day with Zhizhi, and the pile grows faster than you'd think.