An inflected preposition (or a conjugated preposition) is a word formed by combining a simple preposition with a personal pronoun. In other words, instead of having two separate forms – a simple preposition and a personal pronoun, you have only one form - an inflected preposition. For instance, in English you say with me, that is the preposition with and the pronoun me are two separate words, but in Scottish Gaelic le ('with') and mi ('I, me') are combined to form just one word: leam 'with me'.
I've chosen an example from Gaelic because it's a language I'm familiar with and also because the use of inflected pronouns is one of its distinctive features, which is the case with all Celtic languages.
This means that when you're learning Gaelic or any other Celtic language, sooner or later you have to memorize the table of all inflected prepositions, or prepositional pronouns as they seem to be called by most coursebooks and dictionaries. You won't get very far without them because they're used in countless idiomatic expressions.
But you have to start somewhere. As an example, I'll give you the inflected forms of the two Gaelic prepositions that are usually taught first because of their high frequency: aig 'at' and air 'on'.
AIG 'at'
(Among other things, it's used to express possession: Gaelic hasn’t got a simple verb 'have', instead things you have are 'at you'.)
agam (aig + mi) 'at me'
agad (aig + thu) 'at you (singular)'
aige (aig + e) 'at him or at it (masculine)'
aice (aig + i) 'at her or at it (feminine)'
againn (aig + sinn) 'at us'
agaibh (aig + sibh) 'at you (plural)'
aca (aig + iad) 'at them'
AIR 'on'
(It's used to express a large number of ideas: for instance names, thirst and hunger, diseases, hurry and many feelings are 'on you'.)
orm 'on me'
ort 'on you'
air 'on him or it (masculine)'
oirre 'on her or it (feminine)'
oirnn 'on us'
oirbh 'on you (plural)'
orra 'on them'
Now that you know both aig and air, you can say 'I love you' in Gaelic:
Tha gaol agam ort. (pronounced: ha gaol akam orsht) 'Is love at me on you'
I guess you may also want to know how to say there isn't love at you on somebody:
Chan eil gaol agam ort. (pronounced: khanyel gaol akam orsht) 'I don't love you'
At which point, you should also learn the phrase: Tha mi duilich (pronounced: ha mee doolikh) 'I'm sorry'. You may be heartless but there's no need to be impolite.
Pronunciation
I decided not to use phonetic symbols not because I have something against them (on the contrary: tha gaol agam air IPA) but because Gaelic sounds are not my main concern here and therefore I chose accessibility over accuracy.
A few notes:
ao in gaol – like oo in fool but with your lips spread not rounded (long high back unrounded vowel)
kh in chan – like ch in Scottish loch
kh in duilich – like h in hew