The Roman society is one built upon bounds.
The civic duties between People and State. The obedience of the family to the Patre Familias. The cooperation between clients and patrons. While the first two, besides the intricacies of Roman Law and the tyranny of the head of the family, would be easily recognizable by modern audiences, the concept of clientela is mostly unknown - at least on the right side of the Law.
The movie The Godfather shows this relationship like no other picture. During his daughter's wedding, Don Vito Corleone receives guests. They ask for a favour and the blessing of the Don, which is magnanimous granted. However, there is the clear message that one day, maybe never, the Don will ask a favour back, and when that time comes, it is a favour that you cannot refuse.
What type of relationship is the one between client and patron? In platonic terms, it is a mutualistic relationship between two individuals that do not belong to the same social strata or family. Romans only believe in friendship between peers, and the client/patron is the best possible relationship that could exist between nonequivalent people. Each morning the patron would open their houses, receive their clients and have them inquire if their services are needed for the day, share a meal with them, offer them small gifts and under extraordinary circumstances there would be exchange of favours.
Why would the client seek patronage from one or more patrons? For starters, to provide for basic civic needs. If you find yourself dragged to court, your patron will provide with a lawyer; you wish to perform a sacrifice and your patron might arrange it in your behalf; if you were the victim of a robber, the patron would gather their clientela and capture the thief; protection, political support, etc. Without having one's own farm, business, workshop or guild membership, a patron is also the most dignified way to make a living; instead of the perceived "temporary slavery" of a salary, a a skilled client whose abilities were well appreciated would be rewarded for their services by their patrons and well regarded by society.
Why would the patron invest in their relationship with clients and seek to expand their clientela? Above all, prestige. Wealth by itself was not the mark of greatness, for those affluent are expected to return it to the City. Be it by financing public works, civic service, and of course, generous patronage. The political power you wielded, enemies you vanquished and accomplishments of your family might shape how you are remembered after death; the quality and quantity of your clientela determines how you fit in life among the Roman society and helps you build a legacy that might last more than the stones and brick piled in your name. Of course, skilled or just numerous clients are a useful resource by themselves: they offer unique services, they tend to be loyal due to their investment in the relationship, and above all, they can vote and lobby according to your own interest.
Clientela is the Law. And whoever controls the Clientela, legislates the Law.
Of course, just like most Republican institutions, the client and patron would be severly strained during its Late period. As the wealth gap increased, patronage was limited to the wealthiest and turned to be a client into a degrading, one-sided proposal. What used to be a bond soon became the shadow the powerful cast over faceless masses; as Rome expanded, foreign nobility, entire cities and even monarchs became the clients of powerful Romans.
Why should you care about the barber of the Aventine when the King of Bithynia is your client?