Example sentences
wǒ我men们rèn认shí识ma吗？
Do we know each other?
wǒ我bù不rèn认shí识tā他。
I don't know him.
About this word
Both characters carry the speech radical 言. 认 is "to recognize, to acknowledge", 识 is "to know, to tell apart", so 认识 is knowing a person or place from experience. The usage split matters most. 认识 is for people you have met (我认识他), 知道 is for facts (我知道他住在北京), and 会 is for skills (我会游泳). 我认识他 means the two of you have met; 我知道他 only means you have heard of him. It is pronounced rènshi, with a neutral second syllable.
The story behind the character
认
认 is the simplified 認: 言 (speech) gives the meaning, 忍 gave the sound. The 玉篇 defines 認 as 識認, to know something on sight. Simplification swapped the heavy 忍 for 人, which sounds close, and shrank 言 to 讠. Speech stayed in the character, which suits a word covering both knowing a face and admitting a fact.
识
识 is 言 (speech) with 戠 giving the sound. Xu Shen's entry reads 識, 常也。一曰知也, constant, and another reading, to know. The second one won. Duan Yucai later argued 常 was a scribal slip for 意, what is in your mind, which is close to knowing. Either way, 认识 is built from speech and a sound.