Hey 
Regarding the explanation of SP delegation, I think it will be better if we can explain the concept of SP first. SP is actually an abstraction of VESTS. When you power up your liquid STEEM, you basically convert your STEEM to VESTS. As the name suggests, having VESTS means you have a vested interest on this platform. VESTS can be thought as stakes on this platform. In traditional finance terms, you can view it as shares of a company.
Why do I say SP is an abstraction of VESTS? It is because there is a STEEM per VEST rate that is inflating over time. You can view the current conversion rate here (the S/V parameter). I think the reason for coining the term SP is to provide familiarity. Many of us do not know (and probably don't care) about VESTS, hence having SP, short for STEEM Power, makes it easier for users to relate to it.
With this understanding, let's move on to the benefit of holding VESTS (again remembering that SP is just an abstraction of VESTS). By holding VESTS, I see 3 key benefits. First, you get to earn from the ongoing inflation. The longer you hold VESTS, the more STEEM you get when you power down. You can view it as a passive income. The inflation rate is around 8.33% per annum right now and will reduce gradually. You can check it here.
Next, holding VESTS allow you to vote. By voting content, you get to earn curation rewards. I consider this active income as you need to make an effort to cast your vote on the content you fancy. Of course, you can do auto-voting, but I do not want to complicate things by discussing auto-voting here. With the recent HF (hard fork), you now also get to vote on proposals. Proposals are submitted by Steemians for projects that they want to start on Steem and require funds. Successful proposals will get funding from the blockchain. All these are done in a decentralized and automated manner. Last but not least, having VESTS allow you to vote for witnesses. The concept of witnesses can be one full article on its own, so I won't touch on that too much. Just remember that witnesses helps to validate transactions on this blockchain.
Finally, holding VESTS also provide you with Resource Credits (RC). Any activity you perform on the blockchain will consume some RC. Your RC will regenerate over time, however, the maximum RC you have is influenced by the amount of VESTS you own. Hence, holding VESTS in turn gives you the right to use the blockchain.
To summarize, VESTS (remember that SP is an abstraction of VESTS) allow you to:
With all these understood, let's talk about delegation and the differences of delegation in traditional companies' shares and Steem VESTS. First, let's explore what ownership of companies' shares give you. Owning shares of companies largely brings 2 benefits. First, the rights to receive dividends, in other words, to share profits of the company. Next, owning shares also allows the individual to vote for resolutions during the companies' general meetings.
For companies shares, you can delegate your voting rights to someone else and have that person represent you in a general meeting. The person can then vote on your behalf. However, when there is a dividend announced, you are still the ultimate beneficiary of the payout.
VESTS on Steem works in a similar way. By delegating VESTS, you allow someone else to use your VESTS to vote on your behalf. However, unlike companies shares (since there is no concept of curation rewards by holding companies shares), the person who helps you to vote gets the curation rewards. The person also gains the RC provided by the delegated VESTS. In other words, the recipient of delegation gains benefits (2) and (3) as mentioned above. However, since the VESTS still belongs to you, you can undelegate anytime and power down to gain the extra STEEM from inflation. So, by delegating VESTS, you won't lose out your benefit (1).
This is quite a long reply, hope it helps :)
RE: MY VERY FIRST TRIP TO SWITZERLAND - one of the most crypto and blockchain friendly place on the planet earth