noun
wooden building blocks; toy blocks
Refers to the physical wooden blocks used as a children's toy, or the activity of playing with them.
子どもが積み木で遊んでいる。
The child is playing with building blocks.
積み木を高く積み上げた。
I stacked the blocks high.
noun
piled timber; stacked wood
Refers to logs or lumber stacked up, not toy blocks. Less common than the toy sense.
山のふもとに積み木が置いてあった。
Piled timber was left at the foot of the mountain.
ブロック is a broader term for any kind of block (plastic, concrete, etc.), while 積み木 specifically refers to wooden building blocks.
Compound of 積み (tsumi, 'piling up', the continuative form of 積む) + 木 (ki, 'wood'). Literally 'piling-up wood'.