The short answer is that they deliver solutions and support. What they sell, primarily, is the ability for someone at your company to call them and say "we have problem X" and they will respond "no problem, we can solve problem X for you", and they will take care of the rest. This usually costs millions of dollars.
Let's say you are a large Fortune 500 company. A bank perhaps, a large retailer or an oil company. Your net worth rivals Amazon. You do not use AWS or GCP, you host your own data centers, and you have for decades. Now let's say you need another few petabytes of storage with global replication, durability, availability, you need hardware delivered, fibre cables routed, software to tie it all together and someone to call when you run into problems or someone on your backend application team can't figure it out. Or maybe you need Oracle and SAP integrated with Active Directory for your 100,000 employees.
Well, these companies will make that happen. Or many other problems you might have, such as building custom applications, implementing tooling, designing systems, whatever. It's kind of like asking "who employs all these personal chefs?! I've been eating for years and I've never needed a personal chef. I just go to the store, buy some groceries, and make food from the recipes I find online!" The thing is that some people just don't want to deal with all that, and they have enough money to make it someone else's problem who has done it before.
I spent five years in this space (in a small consultancy that was acquired by GlobalLogic last year). I think this is how one of our salespeople might describe the process.
The reality tends to be somewhat messier. I especially disagree with the "personal chef" analogy. A personal chef is an expensive, dedicated, long-term employee - much closer to a full time SWE than to a consultancy. It's more like hiring a catering company for a wedding.
You're right, that would have been better. I certainly didn't mean to imply this process always goes smoothly, or that the quality of the work they provide is without question.
When I started down the Fortune 500 consultancy path, the quality (or lack thereof) used to bother me a lot, then I realised that most customers don't really care, what they want is something that makes their core business run, doesn't matter how.
As long as their core business and KPIs remain untouched, and no scalations take place, everything is fine.
Let's say you are a large Fortune 500 company. A bank perhaps, a large retailer or an oil company. Your net worth rivals Amazon. You do not use AWS or GCP, you host your own data centers, and you have for decades. Now let's say you need another few petabytes of storage with global replication, durability, availability, you need hardware delivered, fibre cables routed, software to tie it all together and someone to call when you run into problems or someone on your backend application team can't figure it out. Or maybe you need Oracle and SAP integrated with Active Directory for your 100,000 employees.
Well, these companies will make that happen. Or many other problems you might have, such as building custom applications, implementing tooling, designing systems, whatever. It's kind of like asking "who employs all these personal chefs?! I've been eating for years and I've never needed a personal chef. I just go to the store, buy some groceries, and make food from the recipes I find online!" The thing is that some people just don't want to deal with all that, and they have enough money to make it someone else's problem who has done it before.