A contig is a contiguous stretch of DNA sequence without gaps that has been assembled solely based on direct sequencing information.
Short sequences (reads) from a fragmented genome are compared against one another, and overlapping reads are merged to produce one long sequence. This merging process is iterative: overlapping reads are added to the merged sequence whenever possible and so the merged sequence becomes even longer. When no further reads overlap the long merged sequence, then this sequence - called a contig - has reached its maximum length.
Contig can be used in other contexts: A contig can be the sequence corresponding to only one clone. A contig map shows the regions of a chromosome where contiguous DNA segments overlap.