Being officially recognized as a member nation by the United Nations is a very important step for many countries to establish themselves as independent nation-states. It confers a number of benefits, but also carries many responsibilities.
The benefits are particularly important for poor countries such as Nepal, because they include various forms of foreign aid, including development assistance and emergency aid for natural disasters. Rich countries such as the United States could probably do without such benefits (indeed usually pay out more in net aid than they receive), but for poor countries they can be a vital lifeline.
When earthquakes devastated Nepal last year, the UN and its member nations stepped in to provide $15 million in disaster aid, which Nepal would not have gotten if they were not a part of the UN.
UN membership also gives a country a vote in the General Assembly, which passes resolutions on a variety of international matters, ranging from trade to war to human rights. Getting one vote among over 200 may not feel like much, but it's much better than having no vote at all.
Being a UN member also provides many symbolic benefits; it establishes your country as an independent nation and projects a sense of openness to be a part of the international community.
Being a UN member carries responsibilities as well; member states must abide by the rules of the UN. They can be sanctioned if they violate these rules, especially with regard to human rights.