Important, Precious, Valuable
noun, な adjective
Think back to the old old olden days. Back when decisions were made with swords. A big cut is going to be important. Just imagine a couple samurai squaring off, then charging, then making one big cut. It's the most important thing they'll do in their lives (if they live!).
たいせつ
This is a jukugo word, which usually means on'yomi readings from the kanji. Since 大 has two on'yomi readings, here's a mnemonic to help you remember which one to use: It's extremely important to keep your ties in sets (たいせつ). If you don't arrange them neatly in sets, the tie police might just come knocking at your door and take you with them!
友人は大切だ。
Friends are important.
これは大切なネックレスなんです。
This is a valuable necklace.
このビー玉、大切にしてね。
Please take good care of this marble.