真っ + [i-adj] / [noun] 真ん + [noun] 真 + [noun]
真 is a prefix meaning "completely" or "exactly". It goes on the front of a colour word, a word for light or dark, or a word for a position, and turns "red" into "bright red" and "middle" into "right in the middle".
The reading depends on the word it joins. Before a k, s or t sound it becomes まっ and doubles that consonant: まっか真っ赤, まっしろ真っ白, まっくろ真っ黒, まっさき真っ先. An h sound also turns into p, as in まっふたつ真っ二つ (まっぷたつ), and まっさお真っ青 gains an s: まっさお. Before n or m it becomes まん: まんなか真ん中, まんまる真ん丸. Elsewhere it stays ま: まよなか真夜中, まうえ真上, まあたらしい真新しい.
The set is fixed. You learn these words one by one; 真 cannot go on any adjective you like, so there is no ×真っ大きい.
Several colour words carry a figurative sense as well. まっさお真っ青 is a face gone pale, まっしろ真っ白 a mind gone blank, and まっかなうそ真っ赤な嘘 a barefaced lie.
With a place or a time, 真 means "exactly": まうえ真上 is directly above, まっさいちゅう真っ最中 the very middle of doing something.