Why it is important to observe if the 10Y treasury yield moves nowadays?

Theoretically there could be many reasons why interest rates increase. I will present you one possible interpretation (this is the one that is currently discussed in the news, see for example NBC):

Democrats have won the congress and accordingly they have the majority to enact their political agenda. Investors believe now this will increase deficit spending for pandemic relieve plans (like the stimulus payments to low income households) or for infrastructure investments. This directly increases the supply of treasuries and prices will fall accordingly. Prices going down means nothing else than an increase in the interest rate.

Why is this potentially problematic? Well in general it isn't, prices simply adjust to the shift in demand and supply. But in this concrete situation it means states have to pay higher interest rates for their debt and this may restrict possibilities to enact investments plans. During the current global pandemic Central banks try to keep interest rates low in order to give governments greater financial leeway.