what type of relationship is there between the nitrogen fixing bacteria found in nodules of legumes and the pl

It's a symbiotic relationship called mutualism. The bacteria converts (i.e.,fixes) atmospheric nitrogen into usable nitrates for the plant ; the legume gives the bacteria an environment in which to thrive.

Its called symbiosis or mutualism, where the two organisms benefit each other from the relationship. The legume plants will provide 'home' for the bacteria, while the bacteria will fixed the Nitrogen from the air into  Nitrate (NO3), which is the available form of nitrogen for the legume plants.

The bacteria belong to the Rhyzobium sp, found in most soil. Rhizobium will only associated with the legume family (leguminoiceae), such as peanut, soybean, mung bean etc.

Root nodules will be formed on the root, where the bacteria (Rhizobium sp) is growing.

Symbiotic relationship between the legume and the Rhizobium speciec is 'specific', meaning  particular Rhizobium  will only associate with particular legume plants only. This is opposite of 'regular' where any nitrogen fixing bacteria can associate with any legumes, which do happened but is very rare.

This kind of relationship had been capitalized in  organic farming system, where legume plants are included in the 'crop rotation program'. The nitrate (NO3) fixed by the bacteria and the legume (of previous crop) can also be used by the 'followed up' crop planted following the legume, in the crop rotation program.

This is one way of saving cost of Nitrogen fertilizer in agriculture,