Size
noun
Words that end with さ are often words that have taken the adjective form (in this case 大きい) of the word and turned into words that describe what the adjective form is doing, if that makes sense. So 大きい (big) goes to 大きさ, and the word that describes what "big" describes is the word size.
おおきさ
When a vocab has okurigana (hiragana attached to the kanji) it is probably going to be the kun'yomi reading. Since you learned the on'yomi reading with the kanji 大, we'll have to use a mnemonic to remember this word.
When you saw the size of (pick something surprising), you said "おお *#$@!" Really imagine something surprising. Say the おお part out loud, as well. Think about the size of whatever you're looking at, too, and how big it is.
このテーブルの大きさは、よこ100センチ、たて120センチです。
The size of this table is 100cm in width and 120cm in length.
テレビの大きさは三十二インチです。
The size of the TV is 32 inches.
ロナルド・マクドナルドはいつも大きさのちがうくつをはいていた。
Ronald McDonald always wore different-sized shoes.