The place of articulation of the consonant /h/ is glottal. The narrowing that produces the friction noise is placed between the vocal folds. When we produce /h/ in speaking, different things happen in different contexts and situations.
Examples: head, ahead, playhouse etc.
For instance, let’s take a look at the word "hat". The /h/ has to be followed by the sound /æ/. When you produce /æ/ sound, the tongue and lips (but not only) position is changed. This change happens simultaneously with the production of /h/ sound so the glottal fricative /h/ has an /æ/ quality.
The glottal fricative /h/ always has the quality of the vowel it precedes. That being said, we can draw the conclusion that phonetically /h/ is a voiceless vowel with the quality of the voiced vowel that follows it.
Phonologically, /h/ is a consonant. It is usually found before vowels or in initial position or in median position. One thing that I think should be mentioned is that when /h/ occurs between voiced sounds (ahead, greenhouse, etc) it is pronounced with voicing. This voicing is not a normal one but it is a weak and fricative sound called breathy voice.
Many people are very sensitive about this consonant. If the /h/ is missing from one’s pronunciation then they tend to judge it as being a sub-standard pronunciation. But, the truth is that most of the English speakers omit /h/ in unstressed pronunciation of the words "her", "he", "him", "his" etc. Only few of them realize that they do this.