Reinforce and provided lateral stability to a wall structure to meet wind, and structural moments. Not there specifically to support weight of the roof system or floor package.
Can be designed in structural foundations or Residential due to lack of wall thickness to provide structural capacities in retaining the pressures of the backfill.
Marcel 
Looks like something installed to deal with a situation that no longer exists. Was this part of the building originally part of the exterior wall? They look like column supports for columns that are no longer in place due to remodeling or construction of an addition.
Kent
It’s a pier and curtain wall construction method–very common in the Carolinas. It’s just different to me in that no wood structure actually rests on them.
What do you think about this one? 1957 house. Brick veneer exterior. One course of brick foundation wall holding up the perimeter of the house and no pilasters. Concern?
Joe, is that a one story house? Are you sure its only one course?
Any cracks or bowing anywhere?
It’s been that way for a long time but not up to todays standards and you don’t want to “own it”.
I would rec. a foundation company that utilizes the services of an engineer to determine the need for lateral reinforcements.
Bruce, if you’re referring to the previous picture, it is one story. The are two courses of brick, but they are not connected as far as I could tell–a gap of about 1.5 inches. The outer course is strictly brick veneer. The inner course is what you see in the picture and it supports the band sil. (It did have cracks all over the outer brick veneer–I did recommend a SE or foundation specialist.)
One course of brick has more than enough material strength to support a 2 story house. The problem is the wall tends to be unstable and buckle/bow as is gets higher, especially if there is unbalanced backfill on one side.
For the pilaster and curtain wall foundation (IRC 404.1.5.1), the piers are spaced as required by IRC R606.8 for lateral stability of the masonry, and there is a limit on the wall height and backfill height. Not common in my area, and I would just use a single wythe concrete block wall and call it a day. In addition to verifying a double rim joist, I also don’t see the straps referenced in the IRC.
For the 1957 house even though the bearing is on the inner wythe of masonry, the outer wythe will help provide buckling/bowing stability if the two are adequately tied together. But the significant cracking is indeed a concern, especially if it’s horizontal cracking near the middle of the wall which is usually an indication of structural overload.
JMO & 2-nickels … 