DNA consists of four bases (adanine, cytosine, guanine and thymine). Three bases in sequence (called a codon) correspond to one amino acid. Obviously, the apparent sequence of amino acids will vary depending on whether you start on the first, second or third base of a codon. Proteins are usually transcribed from a particular starting point and will only make sense as such (there are some exceptions - see the frameshift paradox). Say we have the sequence

AGA TTA ACA TTA GCA

this will translate to

Arg, Leu, Thr, Leu, Ala

However, if we delete one base:

AGA TTA AAT TAG CA

We now have

Arg, Leu, Asn, Stop

The sequence alters where the deletion took place, and we hit a stop codon where previously there wasn't one. This off by one sort of error is known as a frame shift.