I am not a native English speaker. Recently i study some phonetics to improve my english pronunciation (and also french which i am currently studying). I noticed many words with phoneme /əl/ sound like [o] to my ears, like "peoPlE" or "canCEL". I feel like the final vowel of "cancel" and "cancer" sound very different. Can anyone explain this ? Thanks
A central lateral approximant, [l], will have an underlying vocalic resonance which can be plotted on a vowel quadrilateral in the same way as a regular vowel. The vocalic resonances of the various [l]s found in different languages vary in terms of their frontness and backness. Those l's whose vocalic resonances are central are usually referred to as 'clear' and those whose resonances are back (and which can therefore be thought of as being velarised) are usually referred to as 'dark'. Standard Englishes, like many other languages, use different allophones of l, depending on where the consonant appears in the syllable. In standard Englishes a dark l, [ɫ], is used in syllable codas and for syllabic consonants. This will have a [o]-like vocalic resonance, which is what the Original Poster has observed.
The consonant /l/ in English is usually realised as an approximant. This means that although the tongue in such instances makes contact with the alveolar ridge, this doesn't prevent the air from flowing freely out of the mouth and there is no increase in intraoral pressure. The resulting sound is therefore phonetically vowel-like. The only difference between the production of an [l] and a vowel is that in the production of an [l] the blade of the tongue makes contact with the alveolar ridge and the side rims of the tongue are lowered and thus the air doesn't leave directly through the front of the mouth but flows out of the large side apertures this creates.
The resulting sound has an underlying vocalic resonance, or vowel-like quality, which, like other vowels, is affected by which part of the body of the tongue is raised and by the distance between this part of the tongue and the roof of the mouth. In other words, it may be described like regular vowels in terms of its closeness or openness along one dimension and its frontness or backness along another.
In most standard Englishes there are two common allophones of /l/. Broadly generalising, the /l/ which occurs at the beginning of syllables is realised with the vocalic resonance of a mid central vowel, something like [ə]. This is usually referred to as 'clear l' and is transcribed just as [l]. The /l/ that occurs at the end of syllables, in syllable codas, has the vocalic resonance of a close-mid back vowel or similar ( it may be anything from [ʊ] to [o]). This is /l/ is traditionally referred to as 'dark l' and is usually transcribed [ɫ].
The original poster has noticed, then, that dark l has the vocalic resonance of a close-mid back vowel. They could have a future career as a phonetician!
It might also be that the Original Poster has been hearing instances of vocalic /l/.
For an increasingly large number of speakers syllable-final /l/ is now realised as a phonetic vowel, [ʊ], referred to as 'vocalic l'. In fact, many traditional RP speakers have long been using a vocalic l after bilabials in words such as people, but are simply unaware of it (and many will vociferously deny it right after producing one). The rise of vocalic l in RP, therefore, might be viewed as the spread of vocalic l to environments where it wasn't previously used.