Space programs are often maligned for being a "waste of money that could go to the benefit of the common people." These critiques, as you seem to suspect, fail to account for the meaningful benefits that such programs produce for ordinary people. The single largest of which is:
TECHNOLOGY TRANSFER
Technology transfer refers to a process by which technological development occurs in one context (usually public works, academic, or defense contexts), but has applications in another (usually private sector) context and so that technology is licensed out to users in that second context. This brings revenues in, but more importantly spreads a given technology broadly into the society such that members of that society may begin to realize benefits.
NASA, for example claims credit for having developed lightweight breathing apparatuses (originally for space suits) which are now used by firefighters, thereby reducing inhalation injuries associated with protecting the public from fires; structural improvements in school bus design using materials engineering knowledge that originated from spacecraft design; surgical robotics technology that arose out of teleoperational robotics for space applications; food safety protocols that have cut Salmonella cases in half since their implementation; and so on.
Trips to Mars are major technological undertakings that require tremendous capacity development in a number of areas. All of those efforts have network externalities for society at large. Could those technologies be developed by other means? Sure. But having a specific, bold goal to focus efforts is an exceptionally good way to spur momentum. Moreover, the costs of these programs are vanishingly small compared to the 'alternative uses for the money' most often proposed.
The Mars Orbiter Mission 2 probe has an estimated mission cost of $73M. That's a lot of money to a person, but it's pocket change to a government. In the United States you'd hear "Why don't we use that money to feed the hungry?"
The SNAP program, one of the US' programs aimed at doing just that, has an annual budget of $79.2B - More than 1000x times the cost of the Indian Mars mission, and (for the sake of an apples-to-apples comparison) three times the cost of the entire NASA budget for the same year. Given the law of diminishing returns, it becomes questionable to assume that diverting those funds to other programs would even get you much in the way of benefit.
All of these factors are part of what public officials weigh when they make decisions to spend public dollars on various programs - including the space programs.
tl;dr - Yes, there are many benefits to ordinary people that result from things like this Mars mission. We don't yet know what they will be, but historically they have tended to be the advancement or refinement of new technologies that meaningfully improve lives.
P.S. A crewed mission to Mars will require us to develop water recycling, and air-cleaning technology that will be pivotal in reversing the damage from climate change and other industrial-pollution-sourced ecological disasters. The sooner we can get boots on the ground on Mars, the sooner we've unlocked the potential to repair our home planet.
