Phylogenetic constraint is a concept of evolutionary biology that has had quite a lot of discussion. Mary McKitrick (1993) has a great way of introducing the concept of phylogenetic constraint:
"in some sense, all evolutionary studies implicate phylogenetic constraint, and reviewing the topic is like trying to catch a greased pig."
How eloquently put.
It means everyone loves talking about phylogenetic constraint but it just goes all over the place and there is no real consensus on what phylogenetic constraint is. So despite all this widely held discussion, phylogenetic constraint remains one of the most difficult and least understood subjects, and possibly one that is actually ill defined as well. The problem is, when we talk about phylogenetic constraint, we are actually talking about some causal factor for a way in which some trait evolves. For instance, we may see some evolutionary changes in skull morphology that is relatively consistent in closely related taxa, thus we may conclude that some phylogenetic constraint is working on this trait preventing it from evolving more disparately from one taxon to another, e.g. in a classic adaptive radiation model. But causation is always difficult to determine if not impossible to confidently assign.
We may not be able to satisfactorily determine if phylogenetic constraint actually is a plausible mechanism in some trait evolution, but we can observe its presumed effects, as phylogenetic conservatism or phylogenetic signal in your phenotypic data. Thus, when many of us say "phylogenetic constraint" we may actually just be talking about an observed phylogenetic conservatism, i.e. some trait that is showing a pattern of evolution consistent with phylogeny. In other words, some trait evolution that shows up as phenotypic difference in two or more taxa that is consistent with the amount of time (or phylogenetic distance) separating these taxa. Phylogenetic conservatism is thus shared characteristics amongst taxa that can predominantly be explained by phylogenetic distance.
The underlying mechanism of phylogenetic conservatism may be due to several causal factors, phylogenetic constraint being one of them (constraint due to developmental, structural, etc. that is shared amongst closely related taxa). But there is another possible mechanism for phylogenetic conservatism in a character, and that would be phylogenetic inertia (as defined by McKitrick (1993)). Characters evolving under phylogenetic inertia would not particularly be under strong selection, and change would be minimal, or in other words, "if it ain't broke, why fix it?". This is a slightly different case from constraint because there isn't really an active constraint working against evolutionary change; there just ain't any selection for that character to change faster than expected. But if there were any evolutionary changes then they would be due to inertia, so more consistent with a random walk model of evolution (i.e. Brownian motion). Under such circumstances, character change is directly proportional to time and thus proportional to branch length (thus differences between phenotypic traits in two or more taxa would be consistent with phylogenetic distance); or the rate of evolutionary change per unit branch length (or time) is constant.
Funnily enough, some widely used methods (maximum likelihood and independent contrasts analysis) actually assume this a priori (i.e. that character evolution conforms to Brownian motion), so before you go on and use these methods in your characters to say something about how characters changed through phylogeny, you really ought to test to see if your character actually does show a strong phylogenetic signal. Because if it doesn't then you may be violating the assumptions of the methods, or these methods aren't suitable for your character. But that's another matter all together.
Anyway, that aside, the terms I used here are probably all used in different contexts elsewhere (e.g. phylogenetic conservatism = phylogenetic inertia) but the point is, these concepts need to be defined well and used to mean specific things.