AD carries the idea of "in the direction of" and combines with many Latin words and roots to make common English words. Notice that the d of ad usually changes into the same letter as the first letter of the following root or word: ad-fix becomes affix, and ad-sign becomes assign.
To ADMIRE a man means literally to wonder at him.
To AFFIX a poster to the wall is to fasten it to the wall.
AGGRESSION against another country is an approach toward it in a hostile manner.
The house ADJACENT to yours lies next to it.
If a girl ATTRACTS admirers, she draws them toward her.
Also: abbreviate, accede, append, assign, attend, and hundreds of other English words, in many of which the meaning of ad is no longer apparent.
SPELLING: As explained above, the D of AD usually changes into the same letter as the first consonant of the following word, thus making a double consonant. For example, the word attract is ad-tract (drawn towards); so it has a double T. On the other hand adapt is simply ad-apt, with one D.
For the same reason, there is only one D in adore and adumbrate, because ad- has combined with orare and umbra. Since these Latin words begin with vowels and not consonants, the D of AD does not double.