What was the Soviet Union trying to accomplish by invading Afghanistan?

not historian but im an Afghan who studied his history. i hope this comment satisfies the rules of this subreddit.

after the saur revolution in afghanistan and the death of Muhammad Daud Khan, Nur-Muhammad Taraki created a communist regime. he established a land reform that limited the amount of land a family could own. this reform gave government claim on ~500k hectares of land. the reform wasn't popular or productive as agriculture harvest saw a huge decrease that left the population poorer and hungry. he disallowed forced marriages and gave women the right to become politicians. this was very unpopular with the extremely religious population. he tried to reach UNESCO plan to reduce illiteracy within 20 years in 4 years which ultimately failed due to lack of teachers, budget, schools and the proper equipment.

he signed a 20 year long treaty of friendship with the soviets after the bloody uprising in Herat where the army had 20-30k civilians massacred. Taraki claimed the uprisings was staged by Khomeini's regime during his visit to Moscow when the uprising was in fact a sudden and spontaneous.

Afghanistan was always a big target in Russia's Foreign policy (the so called Great Game) but it ended after Great Britain lost their south Asian colonies. Afghanistan was now a Leninist/communist country and the Soviets intended to keep it that way but they denied the Afghani request for military involvements repeatedly. this was mostly due to the fact that they did not agree with Taraki (and his successor Hafizullah Amin) on many things such as the ruling communist party in afghanistan were not "unified" something Brezhnev insisted upon many times to Taraki. the Soviets at first sent up to 500 military/civilian advisor and specialists to Afghanistan to help Afghanistan keep itself strong.

since Daud khan (the centrist predecessor) kept pressing his claims to a united "pashtunistan" on Pakistan, Pakistan now in retaliation, saw an opening to weaken Afghanistan and increase their own role in the region. the Pakistanis increased the ongoing ISI operations (since 1974) to strengthen the nation wide rebelion.

in 1979 the situation were worsened when the US diplomat Adolph "Spike" Dubs was kidnapped by 4 radical communists (a faction called settam-i-melli). USA of course put huge pressure on the afghan government in order to release their ambassador. during the negotiations between the radical communist faction and the US, the afghan security forces "led" by soviet advisors attacked and opened fire at the hotel where the negotiations were undergoing. the ambassador was caught dead in the firefights which further strained the relations between the two superpowers.

USA now hugely backing the mujahedeen through pakistani operations forced soviets to firstly ensure the safety of the government (upon its request) by sending an airborne battalion without combat gears disguised as technical especialists to become personal bodyguards of Taraki. with each months Afghan government started requesting the deployment of bigger and larger land forces . after the assassination of Taraki, Hafizullah Amin became the new leader. the Soviets deployed special KGB operations to test the waters for possible invasion and the reports claimed that the political opponents were being purged, that Hafizullah Amin's loyalty to Soviets is very questionable and that his leadership would become oppressive overtime although Amin always showed official support for the soviets.

but it was mostly the failure of the first and second "Strategic Arms Limitation Talks" (SALT) lead to the military invasion of Afghanistan to "preserve" and "stabilize" the country.

edit: sources:

Afgantsy: The Russians in Afghanistan, 1979-89 by Sir Rodric Braithwaite (former British ambassador to Moscow)