Simply put, the term "phenolic" relates to a cross-linked plastic polymer formed from aromatic hydrocarbons that are similar in some respects to some alcohols. The phenols are usually derived from oil produced from the ground but can be made from other organic materials as well. When the phenol molecules are made to bond, or cross-link, with one another (similar to what happens with common epoxy glue) we get the plastic resin that hardens into a solid mass that can be used for multiple purposes, including counter tops, circuit boards, billiard balls, etc. Phenolic is also a good insulator of heat and electricity. Most of us have seen it all our lives as the black plastic handles on pots and pans.
Micarta is the general term used when the phenolic resin is used with laminations of paper or cloth (like linen) that act similarly to fiberglass in adding structural strength to the material. Micarta has been used for many years in all sorts of applications, and will be familiar to many of us as one of the more common materials used for the handles of knives, including expensive full-tang custom knives. It is a great material for bow risers where additional strength is needed. Some bowyers, like Bob Morrison, sometimes form risers entirely from phenolic Micarta.
The phenolic or Micarta materials feel warmer in your hands than metal, are relatively strong and stable, are not easily damaged, are resistant to heat, cold and chemicals, are denser (heavier) than wood. These materials are ideal for use in many outdoor applications such as knives and bows. Gregg Coffey who makes the Shrew bows (as well as a number of other bowyers) insists on using at least a lamination of phenolic in the handles of his two piece bows to add strength for the BowBolt that is inserted into the two sides of the riser. The phenolic material can also be very attractive and mates well with the aesthetics of many woods. The black Micarta has an appearance in the risers that is similar to Gaboon ebony, but has much greater strength and stability. Just ask "Irish" about that!
Hope this helps.
Allan