Functional DNA is the opposite of junk DNA. It is DNA that does something.
For a time we thought that as much as 98% of our DNA was non-functional, that it didn't code for anything. We have since found any number of ways that supposed 'junk' DNA performs important functions, and hints that there is still more to learn. There is certainly non-functional DNA -- lots of it -- but we are steadily finding that that category is smaller than we thought.
1.5% of our genome is translated1 into proteins, the basic building blocks of every part of our body. This DNA is the most clearly functional, and this is what many scientists had focused on in the past. However, there is more...
27% of the genome is transcribed1 into 'support molecules', part of the protein-coding process but not translated into proteins themselves; this includes ribosomal RNA (rRNA), microRNA (miRNA), and transfer RNA (tRNA). This qualifies as functional DNA, but may also be termed 'noncoding RNA' (ncRNA), as it doesn't directly code for proteins. The following category is also considered a type of ncRNA:
25% of the genome is transcribed but not translated, and is not associated with protein-coding genes in any known way. This segment of the genome is a mystery, as we have very few clues as to why the cell would spend the time and energy to transcribe something that it can not use. We do have some hints; this category includes some ncRNA involved in gene inactivation on sex chromosomes, where one X chromosome in females is inactivated. This is a type of imprinted gene, and ncRNA segments are probably involved in regulation of many, if not all, imprinted genes. This category also includes antisense RNA. DNA consists of two strands, but RNA will nearly always copy from only one strand. If the other strand is coded, it is transcribed in the opposite direction, resulting in antisense RNA, which appears to be used in some cases to inhibit the regularly coded RNA. Pseudogenes are also transcribed; these are assumed to be genes that once were functional and now are not, but this may be an oversimplification. More study is required, but pseudogenes are generally counted as junk DNA.
Exactly what percent of our DNA is functional is up for debate at this point. Recent findings from research comparing chimpanzees and humans suggest that 'junk DNA' may be a more slippery term than we had ever imagined, as it appears that the amount and placement of segments of junk DNA (introns) effect the way that the surrounding chunks of functional DNA (exons) are expressed, and that these emergent properties of RNA expression may be the primary difference between us and chimps. It is now believed that at least 50% of our genome is functional, and it may be much higher than that.
1. Transcription = DNA → RNA; Translation = RNA → protein.
References:
Wellcome Trust: Small RNA: Big News By Richard Twyman.
Wikipedia: Non-coding RNA
Wikipedia: Antisense RNA
Wikipedia: RNA Splicing
ScienceDaily: 'Junk DNA' Defines Differences Between Humans and Chimps
ScienceDaily: Humans And Chimps Differ At Level Of Gene Splicing