Sumti are the parameters of a lojban selbri, or relationship. In other words, a sumti is a "slot" which is filled with an object pertaining to the relationship described in the brivla. The number of sumti in a bridi depends on the brivla used. There can be as few as one or as many as five sumti for a given brivla. By convention, each sumti is labelled in the form x1 for the first sumti, x2 for the second, and so forth up to x5.
- For instance, in the bridi:
- .i mi cu pencu le stizu
- The selbri is pencu, which has four sumti. Sumti x1 is the toucher, the one initiating the touch. Sumti x2 is the one being touched, the recipient. Sumti x3 is the location on x1 that is doing the touching. Lastly, x4 is the location on x2 that is being touched. Beginning at the start of the sentence, we see that mi, "I/me" is x1, and le stizu, "the chair" is x2. Therefore, the bridi means "I touch the chair."
Each sumti is optional, only serving to provide additional details or context when used. Omitting a sumti is typically equivalent to saying that it is "unspecified". Note that this is not the same as specifying "any" or "something". Except where context would suggest otherwise, omitting a sumti is meant to be as vague as reasonably possible.
Sumti Conversion 
In our example above, .i mi cu pencu le stizu ("I touch the chair"), the emphasis rests on the toucher, mi. In English, the emphasis can also rest on the one being touched, i.e. "The chair is touched by me." In English this is considered "passive voice" and is sometimes regarded as poor syntax. However, in lojban, such a construction is perfectly acceptable.
This change is known as a sumti conversion. By swapping sumti, we can reorder them to change the emphasis of the bridi. There exist four cmavo to perform this operation, se, te, ve, and xe, corresponding to swapping x2, x3, x4, and x5, respectively, with x1. To put the emphasis on the chair being touched, we could say ".i le stizu cu se pencu mi"
This operation can be chained if necessary, making each swap one at a time, but such sytax can get confusing very quickly. For instance, ".i le stizu cu se ve te pencu le trixe mi" swaps sumti in the following manner:
- x1 x2 x3 x4
- Swap x2 and x1
- x2 x1 x3 x4
- Swap x4 and x1
- x2 x4 x3 x1
- Swap x3 and x1
- x2 x4 x1 x3
Which results in "The chair was touched in the back by me".
While this bridi is syntactically valid and a reasoable meaning to convey, it is an unwieldy and unnecessariily confusing construct. Fortunately, there is a more straightforward manner of indicating sumti position in a bridi.
Sumti Place Tags 
When the speaker wishes to use multiple sumti out of order such as in the above example, "The chair was touched in the back by me", there is a much simpler way than sumti conversion. A speaker can explicitly state which sumti is being specified by preceding it with its tag, fa, fe, fi, fo, and fu, corresponding to x1, x2, x3, x4, and x5, respectively.
For the above example, the speaker can say ".i fe le stizu cu pencu fo le trixe fa mi". Since the context of the sumti tags is not known until the selbri is encountered, the audience may find it hard to parse. Instead, the speaker could just as easily say ".i pencu fe le stizu fo le trixe fa mi" in order to communicate the relationship to the audience so they can fill in the sumti as they arrive. Both bridi are semantically identical, although the latter may be easier to understand when spoken.
Outside of Selbri 
While the significance of each sumti derive from their usage in selbri, they also have paramount importance when the corresponding brivla is not used as a selbri. When one says "le pencu", which means "the toucher", the meaning actually comes from the x1 sumti of the brivla pencu. So, if one wants to say "the thing which is touched", the speaker could instead say "le se pencu", or "le selpe'u" for short, by converting se and pencu into their rafsi forms sel and pe'u.
Most cmavo operate on the x1 sumti of the brivla, and so sumti conversion is extremely important in composing lojban.